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OPTICS LETTERS / Vol. 39, No. 9 / May 1, 2014
Highly efficient metal grating coupler for membrane-based integrated photonics V. Dolores-Calzadilla,* D. Heiss, and M. Smit Photonic Integration, Department of Electrical Engineering, Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, The Netherlands *Corresponding author: [email protected] Received March 4, 2014; revised April 2, 2014; accepted April 2, 2014; posted April 3, 2014 (Doc. ID 207672); published April 30, 2014 We present the design of a metal grating coupler compatible with membrane photonic circuit platforms, consisting of a buried metal grating and a metal mirror. A nonapodized design provides a fiber-to-chip coupling efficiency at 1.55 μm up to 73%, whereas apodized designs show theoretical efficiencies as high as 89%, with a 3 dB bandwidth of 61 and 78 nm, respectively. An important advantage is that the coupling efficiency is independent from the underlying layer stack, enabling its use in diverse applications. For example, a thin buffer layer is required to achieve optical coupling for the heterogeneous integration of III–V and silicon photonics, whereas a thick buffer is of interest for thermal isolation between photonic membranes and CMOS circuits. © 2014 Optical Society of America OCIS codes: (130.0130) Integrated optics; (130.3120) Integrated optics devices. http://dx.doi.org/10.1364/OL.39.002786
Grating couplers are an alternative to end-fire coupling in integrated photonics to couple light in and out of a photonic circuit. They are used in a variety of applications, for example, on-wafer characterization and packaging [1,2]. They are also attractive for optical interconnect systems that make use of chip-to-fiber and chip-to-chip coupling schemes [3,4]. In membrane-based photonic platforms, grating couplers are of special interest as they allow for mode matching between photonic wires and optical fibers without the use of lenses and spot-size converters [5]. In this respect, the technological development of complementary metal-oxide semiconductor (CMOS) has made silicon on insulator (SOI) a natural choice for passive circuits. On the other hand, InP-membranes on silicon (IMOS) have been proposed as an approach that combines both passive and active components in a single photonic platform [6]. Grating couplers are used in both platforms, however, there are a few issues that typically limit their performance, which are: a mode mismatch between the optical mode in the membranewaveguide and the optical fiber, power leakage to the substrate, and free space diffraction. Several designs have been proposed to improve their coupling efficiency and broadband operation, from shallow etched gratings which are simple in terms of design and fabrication [7], to fully etched complex gratings based on nanostructures whose main advantage is their fabrication with a single etching step [8], and metal-based grating couplers [9–11]. Among the metalbased grating couplers, a design stands out where a metal layer is placed at the bottom of the buffer layer to reflect the downward diffraction, which increases the coupling efficiency up to 78% [9]. Another design consists of a metal grating deposited on top of a waveguide by liftoff. The metal elements produce a strong coherent scattering and calculated efficiencies up to 60% with a 1 dB bandwidth of 40 nm have been reported [10]. While these designs exhibit better coupling efficiencies than dielectric gratings, the efficiency is strongly dependent on the buffer layer thickness below the photonic membrane. 0146-9592/14/092786-04$15.00/0
More recently, a buried metal-based grating was reported, which forbids diffraction to the bottom due to a photonic bandgap effect, using the grating as a one-dimensional metallic photonic crystal [11]. The coupling efficiency in this approach is independent of the buffer layer thickness, but it requires a 600 nm thick metal grating. Fabricating metal gratings with the required width below 300 nm in such thick layers is extremely challenging using standard lift-off or etching processes. In this Letter, we propose a metal grating coupler for TE polarization compatible with both SOI and IMOS, consisting of a thin buried metal-grating and a metal mirror layer which inhibits power leaking into the substrate. It results in a highly efficient grating coupler independent from the buffer thickness, which can be easily fabricated using standard processes. The approach provides the flexibility needed in a variety of applications. For example, a thin bonding layer is usually required to couple light generated in a III–V membrane to a silicon waveguide beneath [12]. A thick benzocyclobutene (BCB), on the other hand, is needed to thermally isolate a photonic membrane from an underlying CMOS circuit. Our grating design works with maximum efficiency in both schemes. Furthermore, the thickness independence relaxes the requirements in the bonding process, simplifying the fabrication technology. The study presented here is based on two-dimensional finite-difference time domain simulations (FDTD). Initially, the grating coupler is optimized for high fiberto-chip coupling. In a second step, apodization schemes are proposed to increase the coupling even further. Finally, the device tolerance is studied to determine the technological challenges for its fabrication. The proposed device has been designed for a 300 nm thick InP-membrane waveguide, however, results for a silicon membrane are very similar. The bonding layer consists of BCB, whose refractive index is 1.54 at 1.55 μm. Figure 1 shows a schematic representation of the metal grating coupler design. It consists of alternating © 2014 Optical Society of America
May 1, 2014 / Vol. 39, No. 9 / OPTICS LETTERS
2787
Fig. 1. (a) General schematic of the reflective metal grating coupler. (b) Main parameters of the grating.
stripes of silver and silicon dioxide below an InP waveguide. In the simulations, we consider 20 periods resulting in a grating length of 12.7 μm, which is enough to provide a good mode size matching with the fiber mode. Furthermore, we consider a 200 nm thick metal mirror. The modeling has been done considering wavelength-dependent refractive index models for InP, Si, and SiO2 [13], as well as for Ag [14]. The metal grating coupler can be fabricated either in a SOI or IMOS platform by a double-side processing similar to the fabrication process reported in [9]. In the first step, the dielectric grating (here made of SiO2 ) is fabricated with e-beam lithography and dry etching on top of the semiconductor wafer of interest. Afterward, the metal layer is deposited by evaporation in a noncritical liftoff process, forming both the metal grating itself and the metal mirror in a single fabrication step. Since silver does not have good adhesion on neither InP nor SiO2 , the deposition of a thin adhesion layer (few nanometers) is required before the actual silver deposition, which could be either Ti, Cr, or Ge. The latter is the best choice as it does not introduce considerable absorption loss to the device. Later, flip-chip adhesive bonding is done on a different substrate by BCB [15]. Then, the initial substrate is removed combining a series of techniques such as lapping and selective wet etching, using the waveguide layer as an etch-stop layer. Finally, the membrane waveguide is e-beam patterned and dry etched. Before performing detailed FDTD studies, we estimated the grating period using the Bragg condition sin θ neff − mλ∕Λ∕nc , where θ is the diffraction angle, neff is the effective index of the mode propagating along the grating, m is the diffraction order, λ is the wavelength, Λ is the grating period, and nc is the refractive index of the cladding (air in this case). Using a mode solver, we calculate the mode index of the modes propagating in the slab regions Air∕InP∕SiO2 and Air/InP/Ag, which are n1 2.7242 and n2 2.5394 0.0008i, respectively, for a 300 nm thick InPmembrane. Considering a 50% filling factor, defined as f f w∕Λ, the grating mode index can be approximated as neff Refn1 n2 g∕2. If we further consider θ 10°, m 1, λ 1.55 μm, and nc 1, it follows from the Bragg condition that the grating period is 631 nm. In the refined 2D FDTD simulations, a grating with period Λ 635 nm and depth d 125 nm results in the highest efficiency at 1.55 μm, as discussed in the following. For
Fig. 2. Coupling efficiency at 1.55 μm as a function of grating depth d for different grating periods, considering f f 50%. The right axis shows the total diffraction efficiency for the case of Λ 635 nm. The inset shows the modulus of the electric field distribution showing the coupling from a fiber to an IMOS waveguide at 1.55 μm.
the simulation, we considered a 9 μm core diameter fiber with an index contrast of 0.005 between the core and cladding, tilted at 10°, placed 10 μm far from the grating, and with an antireflective coating for 1.55 μm at the tip. The optical fiber mode is excited and the power coupled into the fundamental mode (TE polarized) of the waveguide is calculated. In order to couple the InP-membrane to the optical fiber with high efficiencies, the grating strength has to be tuned to get a good match between the exponentially decaying mode in the grating and the fiber mode. Figure 2 shows the coupling efficiency as a function of the grating depth d for different grating periods. We calculate a peak efficiency of 73% when d 175 nm and d 125 nm, for Λ 630 nm and Λ 635 nm, respectively. The latter case is preferred, as it keeps a shallow grating depth which could simplify the fabrication. As a reference, Fig. 2 also shows the total diffraction efficiency of the grating for the reciprocal case, i.e., when the light is diffracted from the waveguide into air. The diffraction efficiency upward increases up to 92% for d > 200 nm. In this case, the residual 8% corresponds to the following contributions: 2% of the power is reflected back into the fundamental mode of the waveguide, 2% is lost by metal absorption, 1% is transmitted through the waveguide, and 3% corresponds to scattering loss at the beginning of the grating coupler. The inset of Fig. 2 shows that there is no power leaking into the substrate due to the presence of the metal layer. Figure 3 shows the spectral distribution of the coupling efficiency for the optimum case (Λ 635 nm and d 125 nm). The result is in good agreement with grating couplers theory, which states that the maximum overlap between a guided mode with ideal exponential intensity distribution and a Gaussian distribution is 80% [5]. The coupling efficiency can be further increased by apodization of the grating. Here, the grating strength is varied along the coupler in order to shape the field decay in such a way that its overlap with the fiber mode is
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Fig. 3. Coupling efficiency for both apodized and nonapodized designs, with Λ 635 nm, d 125 nm, and f f 50%. The filling factor of apodized designs is shown in Table 1.
maximized. Since the power decays exponentially as it propagates along a grating coupler with constant strength, this can be achieved by varying the grating strength from weak to strong along the direction of propagation. The apodization of the grating can be performed with any parameter that influences the grating strength. We varied the filling factor because it is easier to change this parameter rather than the grating depth during fabrication. Table 1 summarizes the investigated apodization models, which were optimized for a high coupling efficiency. All of them consist of a formula to calculate the filling factor along the grating, where n is the number of grating period (varying from 1 to 20) and α is the tuning parameter. We optimized the α values to maximize the coupling efficiency for the different models. The resulting α values and peak efficiencies are shown in Table 1, columns 3 and 4, respectively. A simple linear apodization which increases the filling factor at a rate of 2.2% per grating period leads to a coupling efficiency of 89%, whereas an increasing exponential model and an asymptotic exponential apodization result in the same peak coupling efficiency. The results of both apodized and nonapodized grating couplers are shown in Fig. 3. As can be seen, the resonant wavelength is slightly redshifted for the case of apodized gratings due to the fact that we varied only the filling factor but kept the periodicity constant. It is interesting to note that these three different apodization models produce a similar result in terms of the spectral efficiency distribution, which is an indication of the high tolerance of the apodization of such a metal grating coupler. Finally, we investigated the tolerance of the nonapodized device on the main parameters that could compromise the grating efficiency due to fabrication defects. The Table 1. Apodization Schemes Apodization Type (1) Linear (2) Increasing exponential (3) Asymptotic exponential
Filling Factor
α Value
η
αn αn − 1 1 − αn
0.022 1.020 0.975
89% 89% 89%
Fig. 4. (a) Tolerance of the grating coupler on the filling factor and (b) the grating depth. Unless the plot states something different, the grating parameters are: Λ 635 nm, d 125 nm, and f f 50%.
filling factor is the most difficult parameter to control, since it depends not only on the electron-beam exposure parameters but also on the wafer layer stack due to the forward and backward electron scattering. Figure 4(a) shows that the variation of the filling factor will produce a wavelength shift as well as an efficiency drop. We observe a reduction by 16% for f f 60%. On the other hand, there is a medium tolerance on the grating depth as shown in Fig. 4(b). Negligible peak shifts and efficiency variations are observed for a grating depth between 125 and 175 nm. Furthermore, we also investigated the tolerance on a fiber height change of 10 μm, which resulted in a negligible efficiency reduction (less than 1%). In conclusion, a metal grating coupler design that is independent from the buffer layer thickness was proposed and optimized for high coupling efficiency with a single-mode optical fiber. The device shows a coupling efficiency of 73% for a nonapodized design and an efficiency as high as 89% for an apodized design with a 3 dB bandwidth of 61 and 78 nm, respectively. In view of its high efficiency, independency from the buffer thickness, and practical fabrication, we believe it represents a promising device to be used in applications for which the power budget is of key importance and layer stack flexibility is required. This work was supported by the EU FP7 project NAVOLCHI and ERC project NOLIMITS. DH acknowledges support by the Marie Curie Actions in the Career Integration Grant NAPOLI. References 1. B. W. Snyder and P. A. O’Brien, Proc. SPIE 8614, 86140D (2013). 2. J. Hofrichter, W. M. J. Green, F. Horst, S. Assefa, M. Yang, B. Offrein, and Y. Vlasov, Proceedings of IEEE International Conference on Group IV Photonics (2011), pp. 127–129. 3. J. Yao, X. Zheng, G. Li, I. Shubin, H. Thacker, Y. Luo, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, Proceedings
May 1, 2014 / Vol. 39, No. 9 / OPTICS LETTERS
4. 5. 6. 7. 8. 9.
of IEEE International Conference on Group IV Photonics (2011), pp. 383–385. J. Kang, Y. Atsumi, T. Sifer, Y. Hayashi, T. Amemiya, N. Nishiyama, and S. Arai, Conference on Lasers and Electro-Optics (2013), pp. 1–2. T. Tamir and S. T. Peng, Appl. Phys. 14, 235 (1977). J. van der Tol, R. Zhang, J. Pello, F. Bordas, G. Roelkens, H. Ambrosius, P. Thijs, F. Karouta, and M. Smit, IET Optoelectron. 5, 218 (2011). D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, Opt. Express 18, 18278 (2010). R. Halir, P. Cheben, S. Janz, D. Xu, I. Molina-Fernández, and J. G. Wangüemert-Pérez, Opt. Lett. 34, 1408 (2009). F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Kraus, and R. Baets, J. Lightwave Technol. 25, 151 (2007).
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10. S. Scheerlinck, J. Schrauwen, F. V. Laere, D. Taillaert, D. Van Thourhout, and R. Baets, Opt. Express 15, 9625 (2007). 11. P. Lin, C.-Y. Wu, and P.-T. Lee, in Advanced Photonics Congress, OSA Technical Digest (Optical Society of America, 2012), paper IM4B.6. 12. S. Keyvaninia, S. Verstuyft, F. Lelarge, G.-H. Duan, S. Messaoudene, J. M. Fedeli, T. De Vries, B. Smalbrugge, J. Bolk, M. Smit, D. Van Thourhout, and G. Roelkens, in Asia Communications and Photonics Conference, OSA Technical Digest (Optical Society of America, 2012), paper PAF4A.3. 13. E. D. Palik, Handbook of Optical Constants of Solids I-III (Elsevier, 1985). 14. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972). 15. G. Roelkens, D. Van Thourhout, and R. Baets, Electron. Lett. 41, 561 (2005).
OPTICS LETTERS / Vol. 39, No. 9 / May 1, 2014
Highly efficient metal grating coupler for membrane-based integrated photonics V. Dolores-Calzadilla,* D. Heiss, and M. Smit Photonic Integration, Department of Electrical Engineering, Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, The Netherlands *Corresponding author: [email protected] Received March 4, 2014; revised April 2, 2014; accepted April 2, 2014; posted April 3, 2014 (Doc. ID 207672); published April 30, 2014 We present the design of a metal grating coupler compatible with membrane photonic circuit platforms, consisting of a buried metal grating and a metal mirror. A nonapodized design provides a fiber-to-chip coupling efficiency at 1.55 μm up to 73%, whereas apodized designs show theoretical efficiencies as high as 89%, with a 3 dB bandwidth of 61 and 78 nm, respectively. An important advantage is that the coupling efficiency is independent from the underlying layer stack, enabling its use in diverse applications. For example, a thin buffer layer is required to achieve optical coupling for the heterogeneous integration of III–V and silicon photonics, whereas a thick buffer is of interest for thermal isolation between photonic membranes and CMOS circuits. © 2014 Optical Society of America OCIS codes: (130.0130) Integrated optics; (130.3120) Integrated optics devices. http://dx.doi.org/10.1364/OL.39.002786
Grating couplers are an alternative to end-fire coupling in integrated photonics to couple light in and out of a photonic circuit. They are used in a variety of applications, for example, on-wafer characterization and packaging [1,2]. They are also attractive for optical interconnect systems that make use of chip-to-fiber and chip-to-chip coupling schemes [3,4]. In membrane-based photonic platforms, grating couplers are of special interest as they allow for mode matching between photonic wires and optical fibers without the use of lenses and spot-size converters [5]. In this respect, the technological development of complementary metal-oxide semiconductor (CMOS) has made silicon on insulator (SOI) a natural choice for passive circuits. On the other hand, InP-membranes on silicon (IMOS) have been proposed as an approach that combines both passive and active components in a single photonic platform [6]. Grating couplers are used in both platforms, however, there are a few issues that typically limit their performance, which are: a mode mismatch between the optical mode in the membranewaveguide and the optical fiber, power leakage to the substrate, and free space diffraction. Several designs have been proposed to improve their coupling efficiency and broadband operation, from shallow etched gratings which are simple in terms of design and fabrication [7], to fully etched complex gratings based on nanostructures whose main advantage is their fabrication with a single etching step [8], and metal-based grating couplers [9–11]. Among the metalbased grating couplers, a design stands out where a metal layer is placed at the bottom of the buffer layer to reflect the downward diffraction, which increases the coupling efficiency up to 78% [9]. Another design consists of a metal grating deposited on top of a waveguide by liftoff. The metal elements produce a strong coherent scattering and calculated efficiencies up to 60% with a 1 dB bandwidth of 40 nm have been reported [10]. While these designs exhibit better coupling efficiencies than dielectric gratings, the efficiency is strongly dependent on the buffer layer thickness below the photonic membrane. 0146-9592/14/092786-04$15.00/0
More recently, a buried metal-based grating was reported, which forbids diffraction to the bottom due to a photonic bandgap effect, using the grating as a one-dimensional metallic photonic crystal [11]. The coupling efficiency in this approach is independent of the buffer layer thickness, but it requires a 600 nm thick metal grating. Fabricating metal gratings with the required width below 300 nm in such thick layers is extremely challenging using standard lift-off or etching processes. In this Letter, we propose a metal grating coupler for TE polarization compatible with both SOI and IMOS, consisting of a thin buried metal-grating and a metal mirror layer which inhibits power leaking into the substrate. It results in a highly efficient grating coupler independent from the buffer thickness, which can be easily fabricated using standard processes. The approach provides the flexibility needed in a variety of applications. For example, a thin bonding layer is usually required to couple light generated in a III–V membrane to a silicon waveguide beneath [12]. A thick benzocyclobutene (BCB), on the other hand, is needed to thermally isolate a photonic membrane from an underlying CMOS circuit. Our grating design works with maximum efficiency in both schemes. Furthermore, the thickness independence relaxes the requirements in the bonding process, simplifying the fabrication technology. The study presented here is based on two-dimensional finite-difference time domain simulations (FDTD). Initially, the grating coupler is optimized for high fiberto-chip coupling. In a second step, apodization schemes are proposed to increase the coupling even further. Finally, the device tolerance is studied to determine the technological challenges for its fabrication. The proposed device has been designed for a 300 nm thick InP-membrane waveguide, however, results for a silicon membrane are very similar. The bonding layer consists of BCB, whose refractive index is 1.54 at 1.55 μm. Figure 1 shows a schematic representation of the metal grating coupler design. It consists of alternating © 2014 Optical Society of America
May 1, 2014 / Vol. 39, No. 9 / OPTICS LETTERS
2787
Fig. 1. (a) General schematic of the reflective metal grating coupler. (b) Main parameters of the grating.
stripes of silver and silicon dioxide below an InP waveguide. In the simulations, we consider 20 periods resulting in a grating length of 12.7 μm, which is enough to provide a good mode size matching with the fiber mode. Furthermore, we consider a 200 nm thick metal mirror. The modeling has been done considering wavelength-dependent refractive index models for InP, Si, and SiO2 [13], as well as for Ag [14]. The metal grating coupler can be fabricated either in a SOI or IMOS platform by a double-side processing similar to the fabrication process reported in [9]. In the first step, the dielectric grating (here made of SiO2 ) is fabricated with e-beam lithography and dry etching on top of the semiconductor wafer of interest. Afterward, the metal layer is deposited by evaporation in a noncritical liftoff process, forming both the metal grating itself and the metal mirror in a single fabrication step. Since silver does not have good adhesion on neither InP nor SiO2 , the deposition of a thin adhesion layer (few nanometers) is required before the actual silver deposition, which could be either Ti, Cr, or Ge. The latter is the best choice as it does not introduce considerable absorption loss to the device. Later, flip-chip adhesive bonding is done on a different substrate by BCB [15]. Then, the initial substrate is removed combining a series of techniques such as lapping and selective wet etching, using the waveguide layer as an etch-stop layer. Finally, the membrane waveguide is e-beam patterned and dry etched. Before performing detailed FDTD studies, we estimated the grating period using the Bragg condition sin θ neff − mλ∕Λ∕nc , where θ is the diffraction angle, neff is the effective index of the mode propagating along the grating, m is the diffraction order, λ is the wavelength, Λ is the grating period, and nc is the refractive index of the cladding (air in this case). Using a mode solver, we calculate the mode index of the modes propagating in the slab regions Air∕InP∕SiO2 and Air/InP/Ag, which are n1 2.7242 and n2 2.5394 0.0008i, respectively, for a 300 nm thick InPmembrane. Considering a 50% filling factor, defined as f f w∕Λ, the grating mode index can be approximated as neff Refn1 n2 g∕2. If we further consider θ 10°, m 1, λ 1.55 μm, and nc 1, it follows from the Bragg condition that the grating period is 631 nm. In the refined 2D FDTD simulations, a grating with period Λ 635 nm and depth d 125 nm results in the highest efficiency at 1.55 μm, as discussed in the following. For
Fig. 2. Coupling efficiency at 1.55 μm as a function of grating depth d for different grating periods, considering f f 50%. The right axis shows the total diffraction efficiency for the case of Λ 635 nm. The inset shows the modulus of the electric field distribution showing the coupling from a fiber to an IMOS waveguide at 1.55 μm.
the simulation, we considered a 9 μm core diameter fiber with an index contrast of 0.005 between the core and cladding, tilted at 10°, placed 10 μm far from the grating, and with an antireflective coating for 1.55 μm at the tip. The optical fiber mode is excited and the power coupled into the fundamental mode (TE polarized) of the waveguide is calculated. In order to couple the InP-membrane to the optical fiber with high efficiencies, the grating strength has to be tuned to get a good match between the exponentially decaying mode in the grating and the fiber mode. Figure 2 shows the coupling efficiency as a function of the grating depth d for different grating periods. We calculate a peak efficiency of 73% when d 175 nm and d 125 nm, for Λ 630 nm and Λ 635 nm, respectively. The latter case is preferred, as it keeps a shallow grating depth which could simplify the fabrication. As a reference, Fig. 2 also shows the total diffraction efficiency of the grating for the reciprocal case, i.e., when the light is diffracted from the waveguide into air. The diffraction efficiency upward increases up to 92% for d > 200 nm. In this case, the residual 8% corresponds to the following contributions: 2% of the power is reflected back into the fundamental mode of the waveguide, 2% is lost by metal absorption, 1% is transmitted through the waveguide, and 3% corresponds to scattering loss at the beginning of the grating coupler. The inset of Fig. 2 shows that there is no power leaking into the substrate due to the presence of the metal layer. Figure 3 shows the spectral distribution of the coupling efficiency for the optimum case (Λ 635 nm and d 125 nm). The result is in good agreement with grating couplers theory, which states that the maximum overlap between a guided mode with ideal exponential intensity distribution and a Gaussian distribution is 80% [5]. The coupling efficiency can be further increased by apodization of the grating. Here, the grating strength is varied along the coupler in order to shape the field decay in such a way that its overlap with the fiber mode is
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Fig. 3. Coupling efficiency for both apodized and nonapodized designs, with Λ 635 nm, d 125 nm, and f f 50%. The filling factor of apodized designs is shown in Table 1.
maximized. Since the power decays exponentially as it propagates along a grating coupler with constant strength, this can be achieved by varying the grating strength from weak to strong along the direction of propagation. The apodization of the grating can be performed with any parameter that influences the grating strength. We varied the filling factor because it is easier to change this parameter rather than the grating depth during fabrication. Table 1 summarizes the investigated apodization models, which were optimized for a high coupling efficiency. All of them consist of a formula to calculate the filling factor along the grating, where n is the number of grating period (varying from 1 to 20) and α is the tuning parameter. We optimized the α values to maximize the coupling efficiency for the different models. The resulting α values and peak efficiencies are shown in Table 1, columns 3 and 4, respectively. A simple linear apodization which increases the filling factor at a rate of 2.2% per grating period leads to a coupling efficiency of 89%, whereas an increasing exponential model and an asymptotic exponential apodization result in the same peak coupling efficiency. The results of both apodized and nonapodized grating couplers are shown in Fig. 3. As can be seen, the resonant wavelength is slightly redshifted for the case of apodized gratings due to the fact that we varied only the filling factor but kept the periodicity constant. It is interesting to note that these three different apodization models produce a similar result in terms of the spectral efficiency distribution, which is an indication of the high tolerance of the apodization of such a metal grating coupler. Finally, we investigated the tolerance of the nonapodized device on the main parameters that could compromise the grating efficiency due to fabrication defects. The Table 1. Apodization Schemes Apodization Type (1) Linear (2) Increasing exponential (3) Asymptotic exponential
Filling Factor
α Value
η
αn αn − 1 1 − αn
0.022 1.020 0.975
89% 89% 89%
Fig. 4. (a) Tolerance of the grating coupler on the filling factor and (b) the grating depth. Unless the plot states something different, the grating parameters are: Λ 635 nm, d 125 nm, and f f 50%.
filling factor is the most difficult parameter to control, since it depends not only on the electron-beam exposure parameters but also on the wafer layer stack due to the forward and backward electron scattering. Figure 4(a) shows that the variation of the filling factor will produce a wavelength shift as well as an efficiency drop. We observe a reduction by 16% for f f 60%. On the other hand, there is a medium tolerance on the grating depth as shown in Fig. 4(b). Negligible peak shifts and efficiency variations are observed for a grating depth between 125 and 175 nm. Furthermore, we also investigated the tolerance on a fiber height change of 10 μm, which resulted in a negligible efficiency reduction (less than 1%). In conclusion, a metal grating coupler design that is independent from the buffer layer thickness was proposed and optimized for high coupling efficiency with a single-mode optical fiber. The device shows a coupling efficiency of 73% for a nonapodized design and an efficiency as high as 89% for an apodized design with a 3 dB bandwidth of 61 and 78 nm, respectively. In view of its high efficiency, independency from the buffer thickness, and practical fabrication, we believe it represents a promising device to be used in applications for which the power budget is of key importance and layer stack flexibility is required. This work was supported by the EU FP7 project NAVOLCHI and ERC project NOLIMITS. DH acknowledges support by the Marie Curie Actions in the Career Integration Grant NAPOLI. References 1. B. W. Snyder and P. A. O’Brien, Proc. SPIE 8614, 86140D (2013). 2. J. Hofrichter, W. M. J. Green, F. Horst, S. Assefa, M. Yang, B. Offrein, and Y. Vlasov, Proceedings of IEEE International Conference on Group IV Photonics (2011), pp. 127–129. 3. J. Yao, X. Zheng, G. Li, I. Shubin, H. Thacker, Y. Luo, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, Proceedings
May 1, 2014 / Vol. 39, No. 9 / OPTICS LETTERS
4. 5. 6. 7. 8. 9.
of IEEE International Conference on Group IV Photonics (2011), pp. 383–385. J. Kang, Y. Atsumi, T. Sifer, Y. Hayashi, T. Amemiya, N. Nishiyama, and S. Arai, Conference on Lasers and Electro-Optics (2013), pp. 1–2. T. Tamir and S. T. Peng, Appl. Phys. 14, 235 (1977). J. van der Tol, R. Zhang, J. Pello, F. Bordas, G. Roelkens, H. Ambrosius, P. Thijs, F. Karouta, and M. Smit, IET Optoelectron. 5, 218 (2011). D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, Opt. Express 18, 18278 (2010). R. Halir, P. Cheben, S. Janz, D. Xu, I. Molina-Fernández, and J. G. Wangüemert-Pérez, Opt. Lett. 34, 1408 (2009). F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Kraus, and R. Baets, J. Lightwave Technol. 25, 151 (2007).
2789
10. S. Scheerlinck, J. Schrauwen, F. V. Laere, D. Taillaert, D. Van Thourhout, and R. Baets, Opt. Express 15, 9625 (2007). 11. P. Lin, C.-Y. Wu, and P.-T. Lee, in Advanced Photonics Congress, OSA Technical Digest (Optical Society of America, 2012), paper IM4B.6. 12. S. Keyvaninia, S. Verstuyft, F. Lelarge, G.-H. Duan, S. Messaoudene, J. M. Fedeli, T. De Vries, B. Smalbrugge, J. Bolk, M. Smit, D. Van Thourhout, and G. Roelkens, in Asia Communications and Photonics Conference, OSA Technical Digest (Optical Society of America, 2012), paper PAF4A.3. 13. E. D. Palik, Handbook of Optical Constants of Solids I-III (Elsevier, 1985). 14. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972). 15. G. Roelkens, D. Van Thourhout, and R. Baets, Electron. Lett. 41, 561 (2005).
